Diffraction integral representation of two-photon-resonant image up-converters

This paper shows that the Fraunhofer diffraction integral can apply in the analysis of two-proton-resonant image up-converters. Next, the imaging of up-converters or field distributions of sum frequency light in any observation plane is discussed. This analytical method makes it possible to analyze some systems or effects which can not be treated by geometrical optics, e.g., suitable up-converters pumped by Gaussian beam, diffractions due to finite apertures, and so on. For an equivalently infinite aperture, the results of geometrical optics must be included in those of the diffraction integral representations. Fourier mode optical systems are also discussed in the same way.